Asimple random sample of size nequals40 is drawn from a population. the sample mean is found to be 104.3, and the sample standard deviation is found to be 18.2. is the population mean greater than 100 at the alphaequals0.01 level of significance?

We conclude that population mean is equal to 100 at the α=0.01 level of significance.

Step-by-step explanation:

Given information:

Sample size, n=40

Sample mean=104.3

sample standard deviation, s=18.2

We need to check whether the population mean greater than 100 at the α=0.01 level of significance.

Null hypothesis:

Alternative hypothesis:

Let as assume that the data follow the normal distribution. It is a right tailed test.

The formula for z score is

Using the standard normal table the p-value at z=1.49 and 0.01 level of significance is 0.068112.

(0.068112 > 0.01) p-value is greater than α, so we accept the null hypothesis.

Therefore, we conclude that population mean is equal to 100 at the α=0.01 level of significance.